Least Common Multiple (LCM) of 180 and 38
The least common multiple (LCM) of 180 and 38 is 3420.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 180 and 38?
First, calculate the GCD of 180 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 38 = 4 remainder 28 |
| 2 | 38 ÷ 28 = 1 remainder 10 |
| 3 | 28 ÷ 10 = 2 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 192 | 3648 |
| 64 and 28 | 448 |
| 121 and 54 | 6534 |
| 143 and 125 | 17875 |
| 86 and 63 | 5418 |